What is the KWIK Framework?
Based on the presentation by Praveen Venkateswaran on the same paper, KWIK framework is any learning algorithm that makes the following:


if it knows (by its learning) the answer already, it does tell that
if it is uncertain, it tells the "I don't know" mark
"I don't know" marks should have an upper limit, which is the accuracy/error term of the algorithm.


The idea is that algorithm has a trainer who knows the correct answers, like in any machine learning case, but the difference is that the algorithm agent should know when it has enough knowledge to give the result right away, and when is time to ask and learn. In learning phase the trainer does not calculate errors, only he gives right answers if asked.

There I see two implications: algorithm should know when it has not all the necessary data to answer (when to use "I don't know" answer) and a mechanism to be sure you're correct when the answer is e.g. 1 or 0 in binary case.

How to put that in mathematics, it varies by your chosen algorithm. Also there is a formal equation set for this, but I leave here only this literal definition to give the basic idea.